The present application claims priority from Korean Application No. 01-57979 filed Sep. 19, 2001, the entirety of which is hereby incorporated by reference for all purposes as if fully set forth herein.
1. Technical Field
The present invention relates to a method of exposing a resist of a photomask substrate to fabricate a photomask used for fabricating a semiconductor device, and more particularly, to an exposure method for correcting line width variation occurring during a development process in fabricating a photomask, and a recording medium in which the exposure method is recorded.
2. Description of the Related Art
Generally, in order to fabricate a photomask used for photolithography, a series of processes using electron beam lithography are performed as follows. First, a blank mask on which an opaque layer and an electron beam resist are sequentially deposited on a transparent photomask substrate made of quartz or glass is prepared. The electron beam resist is then exposed to an electron beam in a desirable pattern using an exposure apparatus. Subsequently, the exposed electron beam resist is developed using a development apparatus. The opaque layer is etched using the electron beam resist pattern as a mask, thereby forming an opaque layer pattern. Thereafter, the electron beam resist pattern is removed, thus completing a photomask.
In such fabrication of a photomask, an opaque layer pattern having a different line width from a desirable critical dimension (CD) is formed due to various factors in the fabrication, and the uniformity of a pattern line width decreases. If photolithography is performed using such photomask having a changing pattern line width or decreasing uniformity due to factors in fabrication, a pattern on a wafer also has changes in line width and decreases in uniformity. Accordingly, a photomask having a changing pattern line width or decreasing uniformity results in a semiconductor defect, thereby decreasing the fabrication yield. Consequently, fabrication cost increases. Therefore, it is necessary to analyze the causes of variations in pattern line width and to perform a corrective exposure.
Representative causes of variations in pattern line width occurring during fabrication are a fogging effect and a loading effect. In a fogging effect, an electron beam resist is diffusely exposed to electron beams reflected from the inside or the surface of an electron beam resist and the bottom of an objective lens of an electron beam emitter, which causes a line width to change. In a loading effect, a line width at a portion having a large loading density (i.e., an exposed area of an opaque layer underlying a removed electron beam resist) is greater than a line width at a portion having a small loading density when the opaque layer is etched.
Existing corrective exposure methods take into account fogging and loading effects. Fogging and loading effects are the causes of a variation in a line width occurring during an exposure process and an opaque layer etching process, respectively, among photomask fabrication processes. However, variation in line width occurring during a development process among the photomask fabrication processes has been neglected. Even if a photomask is fabricated by a corrective exposure method in consideration of fogging and loading effects, there is a limitation in increasing the uniformity of pattern line width. Accordingly, even if line width variation occurring during a development process is small, the line width variation exerts an influence which cannot be neglected in the fabrication of highly integrated circuits.
FIG. 1 is a schematic diagram of a development apparatus for explaining variation in line width during a development process.
Referring to FIG. 1, in a state in which a blank mask 20 is put in the development apparatus such that its exposed surface 25, that is, an electron beam resist exposed by an exposure process, faces upward, a developer 10 is ejected through a nozzle 15 downward. Here, the blank mask 20 is rotated, as denoted by the arrow 30, so that the developer 10 can be uniformly distributed. In other words, a spinning process is a general development process. However, when the developer 10 is ejected while the exposed blank mask 20 is rotated, line width uniformity of an opaque layer pattern changes due to variations in the flow velocity, relative flow rate, and heat of vaporization of the developer 10 on the exposed surface 25 of the blank mask 20. Since a spinning process is the development process, the pattern line width changes in a radial direction during the development process. A variation in the pattern line width during the development process decreases the processing margin of a wafer and weakens the cells at the edge of the wafer. Accordingly, the development of a corrective exposure method overcoming the above problems is desired.
To solve the above-described problems, it is a first object to provide an exposure method for correcting pattern line width variation occurring during a development process, after electron beam exposure.
It is a second object to provide a recording medium for recording an exposure method for correcting pattern line width variation occurring during a development process.
To achieve the first object in one embodiment, there is provided an exposure method for correcting pattern line width variation. In the method, a measuring pattern is formed on a photomask substrate according to a test pattern having a predetermined line width. The photomask substrate on which the measuring pattern is formed is divided into meshes. The line width of the measuring pattern in each mesh is measured. Pattern line width variation xcex94CD, which is a difference between the measured line width and the line width of the test pattern, is determined. Thereafter, a graph of the distribution of pattern line width variation xcex94CD(r) measured for each mesh, separated from a reference mesh by a distance r, is made from the graph. From the graph, pattern line width variation xcex94CD(x) at an arbitrary point, separated from the reference mesh by a distance x on the photomask substrate, is estimated. Pattern line width data is corrected with respect to each point on the photomask substrate such that a pattern line width increases in an area where the estimated pattern line width variation xcex94CD(x) is negative, and a pattern line width decreases in an area where the estimated pattern line width variation xcex94CD(x) is positive. The pattern line width data corrected with respect to each point on the photomask substrate is applied to an exposure apparatus.
To achieve the first object, in another embodiment there is provided an exposure method for correcting pattern line width variation. In the method, a standard deviation "sgr" of pattern line width variation xcex94CD(r) is calculated by dividing a photomask substrate into meshes and assuming that the distribution of the pattern line width variation xcex94CD(r) for each mesh, which is separated from a reference mesh at the center of the photomask substrate by a distance r, is a Gaussian distribution expressed by the following equation:             Δ      ⁢              xe2x80x83            ⁢              CD        ⁢                  (          r          )                      =          A      +              B        ·                  exp          ⁡                      [                          -                                                r                  2                                                  σ                  2                                                      ]                                ,
wherein A and B are constants.
Thereafter, the calculated standard deviation o is combined with the above equation, and from the above equation pattern line width variation xcex94CD(x) is estimated at an arbitrary point, separated from the reference mesh by a distance x on the photomask substrate. Pattern line width data is corrected with respect to each point on the photomask substrate such that a pattern line width increases in an area where the estimated pattern line width variation xcex94CD(x) is negative, and a pattern line width decreases in an area where the estimated pattern line width variation xcex94CD(x) is positive. The pattern line width data corrected with respect to each point on the photomask substrate is applied to an exposure apparatus.
Preferably, in calculating the standard deviation, a measuring pattern is formed on the photomask substrate according to a test pattern having a predetermined line width, and a line width of the measuring pattern is measured with respect to each mesh. The pattern line width variation xcex94CD(r), which is a difference between the measured line width and the line width of the test pattern, is determined. An arbitrary "sgr" is selected and combined with the equation to calculate pattern line width variation for each mesh. A deviation between the calculated pattern line width variation and the measured pattern line width variation xcex94CD(r) is calculated to determine the value for "sgr" that minimizes the deviation.
To achieve the second object, in one embodiment there is provided a computer-readable recording medium for recording an exposure method for correcting pattern line width variation in the form of a program. The program includes a program module for dividing a photomask substrate into meshes and making a graph of the distribution of pattern line width variation xcex94CD(r) for each mesh separated from a reference mesh by a distance r; a program module for estimating from the graph pattern line width variation xcex94CD(x) at an arbitrary point, separated from the reference mesh by a distance x on the photomask substrate; a program module for correcting pattern line width data with respect to each point on the photomask substrate such that a pattern line width increases in an area where the estimated pattern line width variation xcex94CD(x) is negative, and a pattern line width decreases in an area where the estimated pattern line width variation xcex94CD(x) is positive; and a program module for operating an exposure apparatus according to the pattern line width data corrected with respect to each point on the photomask substrate to expose an electron beam resist on the photomask substrate.
To achieve the second object, in another embodiment there is provided a computer-readable recording medium for recording an exposure method for correcting pattern line width variation in the form of a program. The program includes a program module for calculating a standard deviation "sgr" of pattern line width variation xcex94CD(r) by dividing a photomask substrate into meshes and assuming that the distribution of the pattern line width variation xcex94CD(r) in each mesh, which is separated from a reference mesh at the center of the photomask substrate by a distance r, is a Gaussian distribution expressed by the following equation:             Δ      ⁢              xe2x80x83            ⁢              CD        ⁢                  (          r          )                      =          A      +              B        ·                  exp          ⁡                      [                          -                                                r                  2                                                  σ                  2                                                      ]                                ,
wherein A and B are constants.
The program also includes a program module for combining the calculated standard deviation "sgr" with the above equation and, from the above equation, estimating pattern line width variation xcex94CD(x) at an arbitrary point, separated from the reference mesh by a distance x on the photomask substrate; a program module for correcting pattern line width data with respect to each point on the photomask substrate such that a pattern line width increases in an area where the estimated pattern line width variation xcex94CD(x) is negative, and a pattern line width decreases in an area where the estimated pattern line width variation xcex94CD(x) is positive; and a program module for operating an exposure apparatus according to the pattern line width data corrected with respect to each point on the photomask substrate to expose an electron beam resist on the photomask substrate.
The program module for calculating may include a sub program module for receiving the pattern line width variation xcex94CD(r), which is a difference between a line width measured in a measuring pattern, which is formed on the photomask substrate according to a test pattern having a predetermined line width, and the line width of the test pattern with respect to each mesh; a sub program module for selecting and combining an arbitrary "sgr" with the equation and calculating pattern line width variation with respect to each mesh; and a sub program module for calculating a deviation between the calculated pattern line width variation and the received pattern line width variation xcex94CD(r), and determining the value of o at which the deviation is minimized.
As disclosed herein, pattern line width variation occurring in a development process with respect to a desirable pattern in fabricating a photomask is estimated, and a corrective exposure is performed so that the estimated pattern line width variation can be corrected, thereby reducing pattern line width variation occurring during the development process. Therefore, the problems of reduction in the processing margin of a wafer and weak cells at the edge of the wafer due to variation in a pattern line width occurring during the development process can be overcome.